Angle-resolved transmission spectroscopy of opal films

The angular behavior of light transmission through opal films over a broad range of wavelengths and angles was investigated. The opal films were prepared using the capillary deposition method (CDM). Many well-defined diffraction peaks were detected and indicate that the CDM results in opal films with high quality. Peaks coinciding at normal incidence split when samples are rotated. The angular shift of these peaks was found to satisfy the kinematical diffraction theory very well. Furthermore, the variation of intensity with incident angle can be interpreted in terms of a simplified dynamical diffraction theory. Moreover, the presence of two differently oriented domains in CDM-made opal films is essential in discussing the measured spectra.

Figure 1

Opal orientation for angle-resolved spectroscopy (ARS) measurement (a) case V, (b) case H. The shaded regions show parts of the samples where measurements were preformed. The angle ${\theta }_{\mathrm{ext}}$ = 0 is normal incidence.

Figure 2

(a) Extinction spectra for selected incident angles and (b) ARS map for the case H (sample: MDN-MA-102-02). The spectra in (a) are the cuts of the ARS map along the indicated lines. The inset is the zoom of the transmittance spectrum at normal incidence showing Fabry-Perot oscillations. Descriptions of the features I, II, and III are given in the text. The scale of color bar will be used in all following ARS maps.

Figure 3

(a) and (b) ARS maps of sample MDN-MA-098-02 with 25 μm thickness for case V and H as indicated. (c) and (d) ARS maps of sample MDN-MA-102-02 (different position as in Fig. 2) with 15 μm thickness for case V and H. All ARS maps use the same scale of color bar as in Fig. 2. Although the H and the V map are qualitatively very similar, there are reproducible shifts in the band crossings and transmission eye positions.

Figure 4

Dark-field images of an opal sample viewed under a stereomicroscope (objective 1.0×2x, working distance 4 cm) with illumination at ∼45° from left (a) and right (b). The arrows with the same color indicate the same features.

Figure 5

Scanning planes for (a) case V and (b) case H. The order of the superscript of the different Gamma points was chosen with increasing distance to $\Gamma$ and due to an appropriate hkl ordering. The dashed lines are special scanning lines for (022)-type ridges that will be discussed in Secs. 4c and 4d.

Figure 6

ARS map with calculated lines for different families of diffraction planes for case V: (a) $\left\{111\right\}$, (b)$\left\{002\right\}$, (c) $\left\{022\right\}$, (d) $\left\{311\right\}$, (e) $\left\{222\right\}$, and (f) selected lines for all families including $\left\{333\right\}$.

Figure 7

ARS map with calculated peaks for different families of diffraction planes for case H. (a) $\left\{111\right\}$, (b) $\left\{002\right\}$, (c) $\left\{022\right\}$, (d) $\left\{311\right\}$, (e) $\left\{222\right\}$, and (f) selected peaks for all families including $\left\{331\right\}$ and $\left\{333\right\}$. The dashed lines are mirror images of solid lines with respect to the ${\theta }_{\mathrm{ext}}=0$ line.

Figure 8

Band structure at the scanning lines (a) ${\Gamma }^1{\Gamma }^{17}$ and (b) ${\Gamma }^1{\Gamma }^2$. The black lines are the corresponding light cones. Some selected external angles are given on the top of the plots.

Figure 9

The $I_{\mathit{TD}}$ and the theoretical gap width for three different peaks and geometries as indicated. The different theoretical curves have been calculated from band structures for opals with a radius of 0.49D (dash-dotted line), 0.50D (solid line), and 0.51D (dotted line). The ideal close-packed opal has a radius of 0.50D.